Metric Geometry

Authors and titles for March 2025

[51] arXiv:2503.07398 (cross-list from math.OA) [cn-pdf, pdf, html, other]

Title: Categorical approach to rigidity of Roe-like algebras of coarse spaces Show Chinese title

Title: 范畴论方法在粗空间的Roe-like代数刚性中的应用

Kostyantyn Krutoy

Subjects: Operator Algebras (math.OA) ; Metric Geometry (math.MG)

[52] arXiv:2503.07448 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Quasi-isometries between graphs with variable edge lengths Show Chinese title

Title: 图的准等距变换与可变边长

James Davies, Meike Hatzel, Robert Hickingbotham

Comments: 7 pages, 1 figure

Subjects: Combinatorics (math.CO) ; Metric Geometry (math.MG)

[53] arXiv:2503.07802 (cross-list from math.FA) [cn-pdf, pdf, other]

Title: The Hellinger-Kantorovich metric measure geometry on spaces of measures Show Chinese title

Title: Hellinger-Kantorovich度量测度几何在测度空间上的应用

Lorenzo Dello Schiavo, Giacomo Enrico Sodini

Comments: 96 pages

Subjects: Functional Analysis (math.FA) ; Metric Geometry (math.MG) ; Probability (math.PR)

[54] arXiv:2503.08411 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups Show Chinese title

Title: 准中图的超平面复形的同伦类型及其在右角Artin群中的应用

Carolyn Abbott, Anthony Genevois, Eduardo Martinez-Pedroza

Comments: 39 pages, 12 figures. Comments are welcome!

Subjects: Group Theory (math.GR) ; Algebraic Topology (math.AT) ; Combinatorics (math.CO) ; Metric Geometry (math.MG)

[55] arXiv:2503.08553 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Energy minimizing harmonic 2-spheres in metric spaces Show Chinese title

Title: 能量最小化调和2球在度量空间中

Damaris Meier, Noa Vikman, Stefan Wenger

Subjects: Differential Geometry (math.DG) ; Metric Geometry (math.MG)

[56] arXiv:2503.08862 (cross-list from math.AT) [cn-pdf, pdf, html, other]

Title: Anti-Vietoris--Rips metric thickenings and Borsuk graphs Show Chinese title

Title: 反Vietoris-Rips度量增厚与Borsuk图

Henry Adams, Alex Elchesen, Sucharita Mallick, Michael Moy

Subjects: Algebraic Topology (math.AT) ; Metric Geometry (math.MG)

[57] arXiv:2503.08995 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: A Combination Theorem for Geodesic Coarsely Convex Group Pairs Show Chinese title

Title: 测地线粗凸群对的组合定理

Tomohiro Fukaya, Eduardo Martínez-Pedroza, Takumi Matsuka

Comments: 45 pages, 7 figures. Comments are welcome

Subjects: Group Theory (math.GR) ; Geometric Topology (math.GT) ; Metric Geometry (math.MG)

[58] arXiv:2503.09195 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Refined algebraic domains with finite sets in the boundaries Show Chinese title

Title: 边界上具有有限集合的精化代数域

Naoki Kitazawa

Comments: 18 pages. 5 figures

Subjects: Algebraic Geometry (math.AG) ; Combinatorics (math.CO) ; Differential Geometry (math.DG) ; Metric Geometry (math.MG)

[59] arXiv:2503.09919 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Drums of high width Show Chinese title

Title: 宽幅鼓

Alex Davies, Prateek Gupta, Sebastien Racaniere, Grzegorz Swirszcz, Adam Zsolt Wagner, Theophane Weber, Geordie Williamson

Comments: 31 pages

Subjects: Combinatorics (math.CO) ; Computational Geometry (cs.CG) ; Metric Geometry (math.MG)

[60] arXiv:2503.10430 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Elementary fractal geometry. 6. The dynamical interior of self-similar sets Show Chinese title

Title: 初等分形几何。 6. 自相似集的动力内部

Christoph Bandt

Comments: 21 pages, 9 figures

Subjects: Dynamical Systems (math.DS) ; Metric Geometry (math.MG)

[61] arXiv:2503.10467 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: Hyperbolic Banach spaces I -- Directed completion of partial orders Show Chinese title

Title: 双曲巴拿赫空间 I -- 偏序的定向完成

Nicola Gigli

Subjects: Functional Analysis (math.FA) ; Metric Geometry (math.MG)

[62] arXiv:2503.11137 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Planar tropical caustics: trivalency and convexity Show Chinese title

Title: 平面热带奇点：三重性和凸性

Mikhail Shkolnikov

Subjects: Algebraic Geometry (math.AG) ; Combinatorics (math.CO) ; Metric Geometry (math.MG) ; Number Theory (math.NT) ; Symplectic Geometry (math.SG)

[63] arXiv:2503.11869 (cross-list from math.PR) [cn-pdf, pdf, html, other]

Title: On the optimal $L_p$-$L_4$ Khintchine inequality Show Chinese title

Title: 关于最优$L_p$-$L_4$Khintchine 不等式

Adam Barański, Daniel Murawski, Piotr Nayar, Krzysztof Oleszkiewicz

Subjects: Probability (math.PR) ; Functional Analysis (math.FA) ; Metric Geometry (math.MG)

[64] arXiv:2503.11987 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Geometric Properties of Periodic Lattices in Function Fields Show Chinese title

Title: 周期格在函数域中的几何性质

Noy Soffer Aranov

Comments: Made minor corrections

Subjects: Number Theory (math.NT) ; Metric Geometry (math.MG)

[65] arXiv:2503.13001 (cross-list from cs.LG) [cn-pdf, pdf, html, other]

Title: Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$ Show Chinese title

Title: 在$\mathbb{R}^2$中分段仿射函数的线性规模神经网络表示

Leo Zanotti

Subjects: Machine Learning (cs.LG) ; Neural and Evolutionary Computing (cs.NE) ; Metric Geometry (math.MG) ; Machine Learning (stat.ML)

[66] arXiv:2503.13829 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: From disc patterns in the plane to character varieties of knot groups Show Chinese title

Title: 从平面中的圆盘图案到纽结群的特征簇

Alex Elzenaar

Comments: 30 pages, 16 figures. v3 improves clarity of figures and fixes minor errors. Correspondence welcomed

Subjects: Geometric Topology (math.GT) ; Group Theory (math.GR) ; Metric Geometry (math.MG)

[67] arXiv:2503.14108 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method Show Chinese title

Title: 关于笛卡尔乘积集的固定Falconer距离问题：抛物线方法

Ji Li, Chong-Wei Liang, Chun-Yen Shen

Comments: 13 pages. Any comment is welcome!!

Subjects: Combinatorics (math.CO) ; Classical Analysis and ODEs (math.CA) ; Metric Geometry (math.MG)

[68] arXiv:2503.15820 (cross-list from math.GR) [cn-pdf, pdf, other]

Title: The Deligne Complex for the $B_3$ Artin Group Show Chinese title

Title: Deligne 用于$B_3$阿廷群的复形

Katherine Goldman, Amy Herron

Comments: 35 pages, 19 figures. Comments welcome

Subjects: Group Theory (math.GR) ; Metric Geometry (math.MG)

[69] arXiv:2503.17337 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Distributional sectional curvature bounds for Riemannian metrics of low regularity Show Chinese title

Title: 低正则性黎曼度量的分布截面曲率界限

Darius Erös, Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso

Comments: 21 pages

Subjects: Differential Geometry (math.DG) ; Metric Geometry (math.MG)

[70] arXiv:2503.17974 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: On a family of hyperbolic Brunnian links and their volumes Show Chinese title

Title: 关于一类双曲布伦尼亚链环及其体积

Dušan D. Repovš, Andrei Yu. Vesnin

Journal-ref: Essays on Topology: Dedicated to Valentin Poenaru, L. Funar and A. Papadopoulos, Eds., Springer Verlag, Berlin, 2025, Chapter 21

Subjects: Geometric Topology (math.GT) ; Metric Geometry (math.MG)

[71] arXiv:2503.18508 (cross-list from cs.CG) [cn-pdf, pdf, html, other]

Title: The Power of Recursive Embeddings for $\ell_p$ Metrics Show Chinese title

Title: 递归嵌入在$\ell_p$度量中的作用

Robert Krauthgamer, Nir Petruschka, Shay Sapir

Comments: 16 pages, fixed minor bugs in Sections 4 and 5

Subjects: Computational Geometry (cs.CG) ; Data Structures and Algorithms (cs.DS) ; Metric Geometry (math.MG)

[72] arXiv:2503.18716 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Bi-geodesic mappings between hyperbolic surfaces with boundary Show Chinese title

Title: 双测地映射在有界双曲曲面之间

Wen Yang

Comments: 23 pages, 17 figures

Subjects: Geometric Topology (math.GT) ; Metric Geometry (math.MG)

[73] arXiv:2503.19652 (cross-list from math.OC) [cn-pdf, pdf, html, other]

Title: Discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces Show Chinese title

Title: 离散时间梯度流在Gromov双曲空间上的无界凸函数

Shin-ichi Ohta

Comments: 15 pages

Subjects: Optimization and Control (math.OC) ; Metric Geometry (math.MG)

[74] arXiv:2503.19792 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Many antipodes implies many neighbors Show Chinese title

Title: 许多对跖点意味着许多邻居

Stefan Steinerberger

Subjects: Combinatorics (math.CO) ; Metric Geometry (math.MG)

[75] arXiv:2503.21325 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: Weak Morse properties in spaces with bounded combings Show Chinese title

Title: 有界组合空间中的弱Morse性质

Cornelia Drutu, Davide Spriano, Stefanie Zbinden

Comments: 30 pages (20 paper, 10 appendix), 8 figures

Subjects: Group Theory (math.GR) ; Metric Geometry (math.MG)